Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups

By D. Greb, Henri Guenancia, Stefan Kebekus. Geometry and Topology, 2017

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We investigate the holonomy group of singular Kahler-Einstein metrics on klt varieties with numerically trivial canonical divisor. Finiteness of the number of connected components, a Bochner principle for holomorphic tensors, and a connection between irreducibility of holonomy representations and stability of the tangent sheaf are established. As a consequence, known decompositions for tangent sheaves of varieties with trivial canonical divisor are refined. In particular, we show that up to finite quasi-etale covers, varieties with strongly stable tangent sheaf are either Calabi-Yau or irreducible holomorphic symplectic. These results form one building block for Horing-Peternell's recent proof of a singular version of the Beauville-Bogomolov Decomposition Theorem.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6f6ff4bc6d4f985c52569692fa1c09dfae31cbc0